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General FourTerminal Network AnalysisAuthor: Leonard Krugman
E_{1} = Z_{11}I_{1} + Z_{12}I_{2} and E_{2} = Z_{21}I_{1} + Z_{22}I_{2} where Z_{11} is the input impedance with the output open. The equivalent current (nodal) equations are I_{1} = Y_{11}E_{1} + Y_{12}E_{2} and I_{2} = Y_{21}E_{1} + Y_{22}E_{2} where Y_{11} is the input admittance with the output shorted. Amplification factors are the best general index of an active network. Since the general case may have amplification in both directions, definitions are included for forward and reverse directions. The forward current amplification factor, α_{21}, is equal to the negative ratio of the current at the shorted output terminals to the current at the input terminals. a_{21} = I_{2}/I_{1} when E_{2} = 0 Then 0 = E_{2} = Z_{21}I_{1} + Z_{22}I_{2}. Solving these equations a_{21} = I_{2}/I_{1} = Z_{21}/Z_{22} and in terms of admittance a_{21} = Y_{21}/Y_{11} The reverse current amplification factor, α_{12}, is equal to the negative ratio of the current at the shorted input terminals to the current at the output terrminals: a_{12} = I_{1}/I_{2} when E_{1} = 0 Then 0 = E_{1} = Z_{11}I_{1} + Z_{12}I_{2}. Solving as before, a_{12} = I_{1}/I_{2} = Z_{12}/Z_{11}, and in terms of admittances a_{12} = Y_{12}/Y_{22} The forward voltage amplification factory, μ_{21}, is equal to the ratio of the open circuit output voltage to the input voltage. , when I_{2} = 0. On this basis, E_{1} = Z_{11}I_{1} and E_{2} = Z_{21}I_{1}. Thus and on an admittance basis The reverse voltage amplification factor μ_{12} is equal to the ratio of the open circuit input voltage to the output voltage. when I_{1} = 0. Then E_{1} = Z_{12}I_{2} and E_{2} = Z_{22}I_{2}. Thus In terms of admittance .


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